Attenuation anisotropy in the linear-slip model: Interpretation of physical modeling data

Abstract

This study attempts to validate a mathematical formalism of introducing attenuation into Schoenberg's linear slip model. This formalism is based on replacing the real-valued weaknesses by complex-valued ones. During an ultrasonic experiment, performed at a central frequency of 100 kHz on a plate-stack model with 1-mm-thick Plexiglas™ plates, the velocity and attenuation ͑inverse of the quality factor Q͒ of P-, SH-, and SV-waves are measured in directions from 25°to 90°with the symmetry axis for dry and oil-saturated models and loading uniaxial pressures of 2 and 4 MPa. The velocity and attenuation data are fitted by the derived theoretical functions. The values of the real and imaginary parts of the complex-valued weaknesses are estimated. The real parts of the weaknesses, which have a clear physical meaning ͑they affect the weakening of the material͒, are three times larger for the dry model than for the oil-saturated one. The imaginary parts of the weaknesses are responsible for attenuation; their values are an order of magnitude smaller than the real parts. The derived expressions for angle-dependent velocities and attenuations can be used to distinguish between dry and oil-saturated fractures. In particular, the P-wave attenuation function in the symmetry-axis direction ͑normal to fracture planes͒ is different in dry and saturated media. The experiment shows that the platestack model is inhomogeneous because of the nonuniform pressure distribution, which degrades the experimental results and creates difficulties in the inversion for the complex-valued weaknesses -particularly in joint inversion of P-and S-wave data.

Fracture-Induced Anisotropic Attenuation

“…(22) with a rotation of p/2 around the y-axis and considering the lossless case ðg ¼ 0Þ: If g 6 ¼ 0; Eq. (22) is equivalent to the medium studied by Chichinina et al (2009b).…”

Critical analysis of theoretical basics of displacement discontinuity model for media with oriented fractures.

“…Модели типа Linear Slip позволяют учитывать не только анизотропию скоростей, но и анизотропию по-глощения, если нормальную и касательную ослаблен-ности и податливости сделать комплексными, т. е. ввести в них мнимые добавки [Чичинина и др., 2006;Сhichinina et al, 2006, 2007, 2009aCarcione et al, 2012aCarcione et al, , b, 2013Gurevich et al, 2009]. Одним из воз-можных механизмов поглощения будет возникающий при распространении волны переток флюида между ориентированными трещинами и изометричными по-рами [Hudson et al, 1996;Pointer et al, 2000;Chapman, 2003Chapman, , 2009.…”

Estimating applicability of the displacement-discontinuity model using experimental data on measurements of elastic-wave velocities

“…3. Его продолжением в сторону низких давлений можно считать график 13 ( ) c P Δ для модели из пласти-нок плексигласа с волнистыми поверхностями, по-строенный нами по данным экспериментальной рабо-ты [Гик, Бобров, 1996], представленным в публикаци-ях [Chichinina et al, 2007[Chichinina et al, , 2009a в терминах модели Шонберга LS. В эксперименте Л.Д.…”